A single occupancy dorm is a room for you on your own. If you prefer space and time alone, then this is the option to pick on your college application. If you are just starting college and want to meet and make friends first and then arrange to share a dorm later, this is also a good option. Part of college life is getting to know new people and sharing experiences, so make sure if you choose single occupancy that you don't just hide away in your room.
Double occupancy dorms are rooms for two people sharing. If you like company and want to experience new things, this may be the option to choose on your application. Sharing a room can be wonderful and life enhancing or it can be difficult, if you and your roommate do not get along or have different ideas about the shared space. If it doesn't work out, you can arrange to move after one semester.
Dorm room standards vary drastically from college to college. Some rooms will be luxurious; others barely fit for purpose. Unfortunately, students do not get much say in where they end up. You will fill in an application asking you about your housing choices but are not guaranteed to end up where you have indicated. Dorms will be allocated and single room occupancy dorms are generally few, so even if you choose single occupancy you might end up sharing.
Even if you get a single room, you will likely have to share other facilities such as the bathroom, kitchen, living and study areas. Privacy is limited in these areas, with most dorm bathrooms large and catering to many students. If you are worried about your food being taken, get a locked box to store it in. Any valuables should also be kept in a locked box and any valuable electrical equipment, such as a laptop, should be attached to something solid with a security cable.